Tracking the geometry of all 597 ammonoid genera from the Lower Devonian into the Lower Triassic, a 145-Myr period that spans three mass extinctions, shows that Paleozoic ammonoid shell geometries were strongly biased for a few combinations of whorl expansion (W), whorl overlap (D), and whorl shape (S). Just three modal combinations accommodated approximately 432 genera (72% of total) and just one combination accommodated 239 genera (40%). All three primary modal forms have similar low expansion rates (W ≈ 1.75) and differ only in coiling tightness (D). These geometries resulted in long body chambers (≈400°) with Nautilus-like static in-life aperture orientations (≈30°) for the great majority (>80%) of Paleozoic ammonoids. The ancestral clade Agoniatitida included a unique spectrum of openly coiled geometries that went extinct at the Frasnian/Famennian boundary (and were not seen again until the Triassic). The Devonian/Mississippian extinction terminated the brief, explosive radiation of the Clymeniida (64 genera). The dominant Paleozoic clade, the Goniatitida (ca. 130 Myr, 374 genera [64% of total]), survived both the F/F and D/M extinctions, but began declining well before the Permian/Triassic crisis. The long-lived Prolecanitida (40 genera [7%]) appeared shortly after the D/M extinction, persisted as a low-diversity clade through the Carboniferous, and gave rise to the Ceratitida in the mid-Permian, from which were derived all Mesozoic ammonoids. After each major extinction event the phylogenetic composition of ammonoid stocks was fundamentally reordered and geometries were recanalized. Without external disturbances, as the relatively uninterrupted Mississippian through Permian record shows, the history of ammonoid shell geometry would probably have been a record of much greater constancy, perhaps tied much more closely to the Lower Devonian geometric landscape.